package euler.p001_050;

import euler.MainEuler;

public class Euler018 extends MainEuler {

    /*
        By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

        3
        7 4
        2 4 6
        8 5 9 3

        That is, 3 + 7 + 4 + 9 = 23.

        Find the maximum total from top to bottom of the triangle below:

        75
        95 64
        17 47 82
        18 35 87 10
        20 04 82 47 65
        19 01 23 75 03 34
        88 02 77 73 07 63 67
        99 65 04 28 06 16 70 92
        41 41 26 56 83 40 80 70 33
        41 48 72 33 47 32 37 16 94 29
        53 71 44 65 25 43 91 52 97 51 14
        70 11 33 28 77 73 17 78 39 68 17 57
        91 71 52 38 17 14 91 43 58 50 27 29 48
        63 66 04 68 89 53 67 30 73 16 69 87 40 31
        04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

     */

    public String resolve(int[][] triangle1) {
        return String.valueOf(maxSum(triangle1,0,0));
    }

    private int maxSum(int[][] triangle, int i, int j) {

        if (i+1 == triangle.length) {
            return triangle[i][j];
        }

        int maxI = maxSum(triangle,i+1, j);
        int maxD = maxSum(triangle,i+1, j+1);

        return triangle[i][j] + Math.max(maxI, maxD);
    }

}
